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Classifying the objects of a mathematical theory requires to make its predicates effective and to automate its computations efficiently so that they are feasible on concrete instances. This is what we propose to do in order to solve problems in relation to numbers, analytic functions, and generating

The study of fine geometric properties of sparse random graphs and of random maps has been a very active field for decades. More recently, a whole branch of the theory has been devoted to the study of random processes living on these objects. In particular random walks, percolation models, Ising and

This collaborative research project aims to bring together researchers from various areas - namely, geometry and topology, minimal surface theory and geometric analysis, and computational geometry and algorithms - to work on a precise theme around min-max constructions and waist estimates. These

The ambition of the ChaMaNe project is to create a research group to achieve significant advances in the field of mathematics for neuroscience. The comprehension of the brain is still far from being achieved and its modeling is extremely complex. In particular, many scales coexist: from proteins and

GeoMod is a Collaborative International Research project between France and Germany. Contemporary model theory studies abstract properties of mathematical structures from the point of view of first-order logic. It tries to isolate combinatorial properties of definable sets such as the existence

This project focuses on the effect of stochastic perturbations on oscillatory phenomena in dynamical systems. Oscillations are present in a vast number of systems in physics, biology and chemistry. Noise acting on these systems may drastically modify the oscillation patterns, or, in the case of e

The objectives of this project are the development and implementation of innovative numerical methods and turbulence models for the simulation of the noise of single-rotor and multi-rotor machines. An important work is to develop low dissipative and low dispersive discretization methods allowing acc

Our project is to treat multiscale models which are both infinite-dimensional and stochastic with a theoretic and computational approach. Multiscale analysis and multiscale numerical approximation for infinite-dimensional problems (partial differential equations) is an extensive part of contemporary

The project Mathematical Physics: mathematics for modern Mathematical Physics (PhyMaths) is a French-Russian project in abstract science. It is made of a French team coordinated by Pascal Hubert and a Russian team coordinated by Senya Sholsman from SkloTech. The project is based on several aspects o

In his address at the ICM in 1994, Maxim Kontsevich stated his Homological Mirror Symmetry Conjecture. This conjecture relates two categories, one from symplectic geometry (the Fukaya category), the other from algebraic geometry (the category of coherent sheaves), via an equivalence of suitably def

Understanding th representations of the absolute Galois group is one of the main problem in number theory. The Langlands program aims to construct a correspondance between Galois representations and representations of algebraic groups (or rather their adelic points) verifying certain conditions. Th

This project concentrates around three themes that are central to the area of modern extreme value statistics. First, we contribute to the expanding literature on frontier modeling in three different directions: Task 1: Polynomial spline fitting of the frontier function under shape constraints.

The aim of this project is to implement a fine analysis of asymptotic behavior of stochastic processes and kinetic equations and use these results in numerical applications. The main issues consist to establish theoretical basis for such studies and to obtain precise quantitative results (optimal t

The project aims in providing Kramers'type law concerning the exit-time of nonlinear diffusions and their associated system of particles when available. More precisely, we are interested in self-stabilizing diffusions (probabilistic interpretation of the granular media equation), in self-interacting

The projet focus on the study and the applications of mulitpliers in non-commutative harmonic analysis. More precisely 1. Intensive study of multipliers a. NC Calderón-Zygmund theory: b. Fourier and Schur multipliers c. Multipliers on quantum groups d. Transference methods We aim t

Dynamics of billiards in rational polygons can be efficiently understood by studying geometrical and dynamical properties of moduli spaces of related differentials (or flat surfaces), using a renormalization process. Quantitative dynamical properties (such as the number of closed orbits, or the diff

This project intend to develop new approaches and conceptual methodology to set up a theoretical sound framework for texture modeling . Texture analysis is a fundamental problem in image processing with numerous fields of applications in medical imaging, computer graphics or data based indexation

The mapping class groups of Riemann surfaces play a predominant role in several fields of mathematics, including algebraic geometry, differential geometry and low-dimensional topology. By a classical result of Dehn, Nielsen and Baer, these groups can be identified with the outer automorphism groups

Physicists are able to describe the world at different scales. At the microscopic level, systems are composed of a huge number of atoms and are studied on time scales which are very large compared to the typical time scales of the atomic degrees of freedom. At the macroscopic level, physical pheno

This project aims at studying advanced algebraic and combinatorial structures associated with walks and heaps of cycles on graph. The outstanding goal here is to calculate the connective and universal constants which dictate the asymptotic growth of the number of self-avoiding walks (SAWs) and polyg

The study of group actions on manifolds is an extension of classical dynamical systems. It is a combination of algebra and dynamics: the algebraic structure makes the dynamics rigid, while the dynamics provide algebraic information. The complexity of the problem leaves us with plenty of unsolved qu

The current project wish to develop new mathematical and numerical methods to solve topology optimization problems for heat transfers in fluid flow. Such kind of problems are mathematically equivalent to optimization problems whose constraints are given by a set of Partial-Differential-Equations and

We will try to: - Classify von Neumann algebras arising from groups and group actions. We hope to make progress on a conjecture of Connes that predicts some rigidity phenomena for higher rank semi-simple lattices; - Understand the structure of these algebras (How non-commutative are they? Do they

Our project aims at going beyond existing results concerning the analysis and the implementation of numerical algorithms for two classes of stochastic partial differential equations: semilinear parabolic like Allen-Cahn, Cahn-Hilliard, Burgers, Navier-Stokes and FitzHugh-Nagumo equations and hyperbo

This project aims at studying, from the mathematical point of view, certain singular asymptotic regimes for Vlasov equations, that is to say for kinetic transport equations without collision. The asymptotic regimes we would like to consider are of two different nature: firstly large time behavior of